Related papers: Two toy models for the motion of a leaky tank car
An exhaustive analysis of the leaky tank car problem is presented, pointing out its intriguing physical properties, which well serve to students and teachers for illustrating standard Newtonian mechanics in a highly non-standard fashion.…
The cage effect is widely accepted as the basic microscopic mechanism underlying the physics of supercooled liquids in contrast with usual liquids which are governed by molecular interactions only. In this work we implement a new toy model…
We extend our previous analysis of the toy model that mimics the mode coupling theory of supercooled liquids and glass transitions to the out of equilibrium dynamics. We derive a self-consistent set of equations for correlation and response…
This work is basically about the general form of Newton's second law for variable mass problems. We develop a model for describing the motion of the one-dimensional oscillator with a variable mass within the framework of classroom physics.…
The one dimensional probabilistic toy model of particle scattering theory is proposed. The toy model version of scattering probability is proved to be equal to the hypervolume of a n-dimensional figure. The solution for any n-particle toy…
Two models of anomalous diffusion of cosmic ray in the leaky-box approximation are compared: one of them is based on the decoupled time-space L\'evy flights and the other on fractional walks with a finite free motion velocity. Distributions…
A geyser can be reproduced by a toy experiment composed of a water pool located above a water reservoir, the two being connected by a long and narrow tube. When the bottom reservoir is heated, the system experiences periodic eruptions of…
We investigate a toy model of liquid, based on simplified HNC equations in very large spatial dimension D. The model does not exhibit a phase transition, but several regimes of the behavior when D\to\infty can be observed in different…
We are concerned with a one dimensional flow of a compressible fluid which may be seen as a simplification of the flow of fluid in a long thin pipe. We assume that the pipe is on one side ended by a spring. The other side of the pipe is let…
A mathematical model is derived for the dynamics of a cylinder, or wheel, rolling over a thin viscous film. The model combines the Reynolds lubrication equation for the fluid with an equation of motion for the wheel. Two asymptotic limits…
Open problems in fluid dynamics, such as the existence of finite-time singularities (blowup), explanation of intermittency in developed turbulence, etc., are related to multi-scale structure and symmetries of underlying equations of motion.…
This paper studies various aspects of the motion of relativistic rotators, both in the presence and absence of external fields, using a toy model which, in a sense, can be regarded as a non-relativistic limit of the rotators. In a simpler…
In the first part of the article, we will outline the paradoxical picture that arises when attempting to calculate the recoil force of the water leakage from a hole at the bottom of a water tank. We will present three different options for…
The nonequilibrium response and fluctuations of Markovian systems, both near and far from equilibrium, are best understood by varying their parameters along dynamical equivalence classes. In this note, I illustrate this approach for an…
A toy model is proposed which incorporates the reversible mode coupling mechanism responsible for ergodic-nonergodic transition with trivial Hamiltonian in the mode coupling theory (MCT) of structural glass transition. The model can be…
We present a model for the dynamics of fluid vesicles in linear flow which consistently includes thermal fluctuations and nonlinear coupling between different modes. At the transition between tank-treading and tumbling, we predict a…
We propose a toy model to reproduce the fractal structure of kink and antikink collisions on one topological sector of $\phi^6$ theory. Using the toy model, we investigate the missing bounce windows observed in the fractal structure, and…
A uni-directional two-lane road is approximated by a set of two parallel closed one-dimensional chains. Two types of car i.e. slow and fast ones are considered in the system. Based on the Nagel-Schreckenberg (Na-Sch) model of traffic flow,…
Chemical equilibrium is fully characterized by thermodynamics, while the rates of chemical reactions can be calculated for ideal solutions by using mass-action equations. The evaluation of the rates of reactions in a non-ideal system is…
A hopping model for molecular motors is presented consisting of a state with asymmetric hopping rates with period 2 and a state with uniform hopping rates. State changes lead to a stationary unidirectional current of a particle. The current…